Anode Plasma Effects on Relativistic Field-Emission-Limited Diodes

In a previous work, we investigated a relativistic field-emission-limited diode employing a high-transparency mesh anode via a self-consistent approach. The field emission process is described quantum-mechanically by the FowlerNordheim equation. The cathode plasma and surface properties are considered within the framework of the effective work function approximation. Space charge effects are described by Poisson's equation including relativistic effects. Ionization effects at the high-transparency mesh anode are ignored. The numerical calculations are carried out on a time scale much shorter than the emergence of the gap closure. We found that the quasi-stationary state of the diode exhibits a cutoff voltage. The electric field on the cathode surface is found to be saturated in the high voltage regime and determined by the effective work function only. However, ionization effects at the anode cannot be eliminated in real world, even for the high-transparency mesh anode. It is well known that the emergence of upstream ion current would enhance the space-charge limiting current. In the present work, we consider the anode plasma effects on the relativistic field-emission-limiting current. The Comparisons of emission characteristics between space-charge-limited and field emission-limited diodes will be given. The ion current in Poisson's equation is treated as a tuning parameter. The J-V and E_s-V curves are plotted for variant ion current, where J is the total current density, V is the diode voltage, and E_s is the electric field on the cathode surface.